I ran into the same type of issue and figured that the Overdue smart queue would help - but unless I am mistaken, there is no "counter" for the Overdue smart queue, so there is no way to tell that it contains any items (other than manually checking every day). Did I miss something?
I did see counters on Inbox and Assignment, but not for Overdue, Due Today, Due in a Week, or All Items. Counters for these would certainly solve my issue with tasks sliding into overdue.
Thanks so much - great software by the way - I have been using Outlook tasks for 20 years and this is the first product that seems to be able to handle most of my (very particular) needs.
RB